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A quasi-sure approach to the control of non-Markovian stochastic differential equations


 
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1. Title Title of document A quasi-sure approach to the control of non-Markovian stochastic differential equations
 
2. Creator Author's name, affiliation, country Marcel Nutz; Columbia University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stochastic optimal control; non-Markovian SDE; second order BSDE; $G$-expectation; random $G$-expectation; volatility uncertainty; risk measure
 
3. Subject Subject classification 93E20; 49L20; 60H10; 60G44; 91B30
 
4. Description Abstract We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This value process is characterized by a second order backward SDE, which can be seen as a non-Markovian analogue of the Hamilton-Jacobi Bellman partial differential equation. Moreover, our value process yields a generalization of the $G$-expectation to the context of SDEs.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-03-19
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1892
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1892
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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